The base of a rectangle lies on the x axis while its upper two vertices are on the parabola y = 10 − x 2 . Suppose the upper right vertex is (x, y). Write the area of the rectangle as a function of x.

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The base of a rectangle lies on the x axis while its upper two vertices are on the parabola   y  =  10  −      x    2  . Suppose the upper right vertex is (x, y). Write the area of the rectangle as a function of x.

Gustavo Zimmerman · Accepted Answer

If the upper two vertices are on the parabola   y  =  10  −      x    2   and the upper right vertex is at (x,y)then the upper left vertex is at (-x,y) and the lowerleft vertex is at (-x,0) and the lower right vertex is at (x,0).In order to find the area we need the length and height of therectangle.Width: The length is going to be 2x. From the lower left vertex you travel x distance to zero, thenanother x distance to the lower right vertex.Heighth: The heighth is going to equal to y which isequal to   10  −      x          2       .Therefore the area is equal to   (  2  x  )  ∗  (  10  −      x          2        )  =  20  x  −  2      x          3

The base of a rectangle lies on the x axis while its upper two vertices are on the parabola y=10-x^2. Suppose the upper right vertex is (x, y). Write the area of the rectangle as a function of x.

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